Question Number 79649 by john santu last updated on 27/Jan/20 $$\mathrm{given}\:\mathrm{a},\mathrm{ar},\mathrm{ar}^{\mathrm{2}} ,\mathrm{ar}^{\mathrm{3}} ,…\:\mathrm{is}\:\mathrm{a}\:\mathrm{GPwith}\: \\ $$$$\mathrm{n}\rightarrow\infty\:,\mathrm{r}\:<\:\mathrm{1} \\ $$$$\mathrm{if}\::\:\mathrm{a},\mathrm{x}_{\mathrm{1}} ,\mathrm{x}_{\mathrm{2}} ,\mathrm{ar},\mathrm{x}_{\mathrm{3}} ,\:\mathrm{x}_{\mathrm{4}} ,\mathrm{x}_{\mathrm{5}} ,\mathrm{x}_{\mathrm{6}} ,\mathrm{ar}^{\mathrm{2}} , \\…
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Question Number 79609 by mr W last updated on 26/Jan/20 Commented by mr W last updated on 26/Jan/20 $${if}\:{the}\:{large}\:{square}\:{has}\:{the}\:{side}\:{length} \\ $$$$\mathrm{10},\:{find}\:{the}\:{radius}\:{r}\:{of}\:{the}\:{smallest} \\ $$$${circle}. \\ $$…
Question Number 14071 by tawa tawa last updated on 27/May/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Partial}\:\mathrm{fraction}\: \\ $$$$\frac{\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{9x}^{\mathrm{3}} \:+\:\mathrm{16x}^{\mathrm{2}} \:+\:\mathrm{9x}\:+\:\mathrm{13}}{\left(\mathrm{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:−\:\mathrm{2}\right)^{\mathrm{2}} } \\ $$ Commented by Tinkutara last…
Question Number 79572 by ajfour last updated on 26/Jan/20 Commented by ajfour last updated on 26/Jan/20 $$\bigtriangleup{ABC}\:{is}\:{equilateral}.\:{The}\:{smaller} \\ $$$${circles}\:{have}\:{radii}\:\mathrm{1}\:{and}\:{a}.\:{Find} \\ $$$${the}\:{circumcircle}\:{radius}. \\ $$ Answered by…
Question Number 79449 by mr W last updated on 25/Jan/20 Commented by mr W last updated on 25/Jan/20 $$\left[{Repost}\:{of}\:{an}\:{old}\:{question}\:{from}\:{b}.{e}.{h}.{i}.\:{sir}\right] \\ $$$${Find}\:{the}\:{radius}\:{of}\:\mathrm{20}{th}\:{circle}. \\ $$ Commented by…
Question Number 13888 by Tinkutara last updated on 24/May/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{A}',\:{B}'\:\mathrm{and}\:{C}'\:\mathrm{are}\:\mathrm{the} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:{BC},\:{CA}\:\mathrm{and}\:{AB}, \\ $$$$\mathrm{respectively},\:\mathrm{then} \\ $$$${AA}'\:+\:{BB}'\:+\:{CC}'\:<\:{AB}\:+\:{BC}\:+\:{CA} \\ $$ Commented by Tinkutara last updated on 24/May/17…
Question Number 79377 by mr W last updated on 24/Jan/20 Commented by mr W last updated on 24/Jan/20 $${the}\:{side}\:{length}\:{of}\:{the}\:{square}\:{is}\:{a}. \\ $$$${find}\:{the}\:{radius}\:{of}\:{the}\:{n}−{th}\:{small} \\ $$$${circle}\:{r}_{{n}} . \\…
Question Number 79368 by TawaTawa last updated on 24/Jan/20 Commented by TawaTawa last updated on 24/Jan/20 $$\mathrm{31}\:+\:\mathrm{105}\:+\:\angle\mathrm{Q}\:\:\:=\:\:\mathrm{180}, \\ $$$$\Rightarrow\:\:\:\angle\:\mathrm{Q}\:\:\:=\:\:\mathrm{44} \\ $$$$\therefore\:\:\:\:\:\:\angle\:\mathrm{S}\:\:+\:\:\angle\mathrm{Q}\:\:\:\:=\:\:\mathrm{180},\:\:\:\:\:\:\:\:\:\angle\mathrm{S}\:\:=\:\:\mathrm{136} \\ $$$$ \\ $$$$\angle\mathrm{P}\:+\:\angle\mathrm{R}\:\:=\:\:\mathrm{180},\:\:\:\:\:\:\:\angle\mathrm{R}\:\:=\:\:\mathrm{180}\:−\:\mathrm{150}\:\:=\:\:\mathrm{30}\:\:\:\left(\mathrm{confuse}\:\mathrm{here}\right).…
Question Number 79365 by mr W last updated on 24/Jan/20 Commented by mr W last updated on 24/Jan/20 $${this}\:{question}\:{was}\:{once}\:{posted}.\:{do} \\ $$$${you}\:{think}\:{that}\:{there}\:{is}\:{an}\:{unique} \\ $$$${solution}\:{for}\:\frac{\Delta_{{KLM}} }{\Delta_{{ABC}} }\:{when}\:{only}\:\frac{{R}}{{r}}\:{is}…